help-0

[minor heath]

yes

[tough prism]

thank you!

i have like 2 more if u can help me out

[minor heath]

$\text{probability of drawing a red, then a green}=(\text{probability of drawing a red marble})*(\text{probability of drawing a green marble})$

[ocean seal]

G3oG0dly

[tough prism]

i got 10/169

[alpine sable]

guys what would this equal?

[minor heath]

yep its correct

[alpine sable]

guys

[tough prism]

ight thanks

1 more

[alpine sable]

would it be

[minor heath]

this channel's occupied

[alpine sable]

oh one person per channel?

[minor heath]

yep

[tough prism]

ok last one

[alpine sable]

mb

[tough prism]

i really appreicate ur help

i tried doing it and got 0.16

[minor heath]

final one: just add all the data that corresponds to either using a car to go to school, or an 11th grader

divide that over the total of all data

[tough prism]

yea i did it got 0.26

i mean 0.16**

that correct?

[minor heath]

still wrong

[tough prism]

arl give me a sec

ok

i got 0.14

correct?

[minor heath]

nope

remember that the total is 325

it says in the bottom right corner

[tough prism]

ok im sorry lmao i think it should be 0.67 now

[minor heath]

there we go

[tough prism]

thanks !

i apprecaite it brodie !

[minor heath]

no problem

[trim oracle]

Can anyone explain to me how to do b, i,ii? I am not sure what the a or b is or what they mean?

[pastel mauve]

first you have to make it into an equation

a parabola equation

search that up there are vids

and then you can take a and b from that

i dont remember exactly

[gloomy lintel]

Well the max point is at (4,20) so b is gonna be 20 straight off the bat

Bc the smallest (x+a)^2 can be is 0

The x value at the max point is 4, so a+4 all squared is 0, a+4 is 0 therefore a=-4

So it’s working backwards from the completed square

[pastel mauve]

can u help with mine too

[rapid horizon]

can someone help me with this. I need help with other ones as well

[alpine sable]

Still need help?

[ocean carbon]

If I know that a number is 3, 4, 2 but these are stored as three separate integers. How could I convert this:

int a = 3;
int b = 4;
int c = 2;

Into :

int x = 342;```

Mathematically.

[rapid horizon]

yeah

i need help on multiple ones this worksheet is confusing

[alpine sable]

ok

so know the measure of arc ab?

and arc ca?

Need a hint?

Inscribed Angle Theorem

[rapid horizon]

well I think we know the measure of bc by multipluing 48 twice?

[alpine sable]

No

You double the value

of 48

What you just said is 48^2

[rapid horizon]

yeah double the value

is what i meant

[alpine sable]

alright

[rapid horizon]

i meant multipling 48 by 2

[alpine sable]

ok you got the measure of arc ab

now what is ca?

[rapid horizon]

wait didnt I just find BC there

[alpine sable]

no

[rapid horizon]

because bc is 48

[alpine sable]

ACB

is 49

48

[rapid horizon]

96 is the arc

[alpine sable]

the corresponding arc is AB

[rapid horizon]

ohh ok

[alpine sable]

what ever is opposite to the angle

[rapid horizon]

yeah so that is 96 because 48 * 2

[alpine sable]

is the arc

corresponding to that angle

ok now

find arc ca

[rapid horizon]

is it 264?

[alpine sable]

no

[rapid horizon]

or wait

that was just subtracting 360 - 96

[alpine sable]

no

[rapid horizon]

so how would i do that

[alpine sable]

You should notice

it's a semicircle

[rapid horizon]

yes

[alpine sable]

what's the measure of the full arc in a semi circle?

180 degs

[rapid horizon]

yes

because its 180

ohh i see

[alpine sable]

It's half a circle

[rapid horizon]

so 180 - 96

[alpine sable]

the measure of the full circle

is 360

[rapid horizon]

yeah ik

[alpine sable]

and a semicircle is just half that

so 180

[rapid horizon]

yeah

[alpine sable]

therefore measure of arc ca is 180

and arc cb

should be obvious to solve

[muted raft]

a * 100+b * 10+c

[rapid horizon]

yeah

[alpine sable]

360-180-96

[rapid horizon]

mhm

[alpine sable]

ok whats the measure of arc cb

[rapid horizon]

84

[alpine sable]

yeah

[rapid horizon]

thanks yeah i was confused i should not have been because it was obviously a semi circle

can you help me on a few others im just having a difficult time on this sheet

[alpine sable]

one moment please

[rapid horizon]

I have a good idea of it though like I marked it out for here, and I know the equation i just dont know the numbers

ok

[alpine sable]

with someone else

[rapid horizon]

ok this is what i marked take your time just putting this here

[alpine sable]

you'll only need 1 theorem here

and that theorem is what you used in the previous question

Inscribed Angle Theorem

[rapid horizon]

yes

ignore the equation to the side

[alpine sable]

ok

so whats stopping you

seems to me like you understand

[rapid horizon]

wait just making sure that

i do

88 + 112 + 114 = 360

and then just find the missing

[alpine sable]

Yes

then half that

[alpine sable]

yes

and no

you're missing a number

therefore making it unequal

[rapid horizon]

yeah ik

im trying to find that number by doing that

[alpine sable]

Add an x

88+112+114+x=360

[rapid horizon]

ok let me just calculate that

314

360 - 314

=46

[alpine sable]

yeah

then half that

[rapid horizon]

so then half that right

[alpine sable]

halve the difference of 360-314

yes

[rapid horizon]

alright thanks

[trim oracle]

can anyone help me with b?

[ocean carbon]

would that work fo r all ranndom numbers withinn range of 0 - 9, inclusive?

[alpine sable]

Just put h = -17 and solve the quadratic equation

Ignore negative solution as time is not negative

[trim oracle]

but i have t and t^2

so idk how I can work out t

oh wait

i use the quadratic formula?

like rearrange so its like ax^2 + bx + c = 0?

[muted raft]

Why would it not?

[ocean carbon]

no idea

lol

like

what if it's 0

what if a , b or c is 0

[trim oracle]

would still work

[muted raft]

100 * 0 + 10 * b + c = bc digit

[trim oracle]

i tried quadratic formula and it didn't work, i think cus negative in square root

[dusk smelt]

@trim oracle you should get t=17/5 and -1

you take the positive answer

if youre getting negative in the square root then youre doing something wrong, show us your work

[dusk smelt]

a=-5

not 5

[trim oracle]

Oops

Ty

[dusk smelt]

np

[finite marsh]

could i get please get some help with these questions?

[alpine sable]

函数等于

我不知道对不起

[finite marsh]

its okay

2.38 is the one I have problems with

[alpine sable]

兄弟能帮我答题吗

[dusk smelt]

cant help if not in english, sorry

[strong furnace]

can you atleast explain what they want from you

[alpine sable]

How to get b and c?

[finite marsh]

in 2.38?

[strong furnace]

any of the parts you need help with

[finite marsh]

well i am not fluent in chinese nor english so take the translations with a grain of salt

[alpine sable]

Please, someone

[finite marsh]

Suppose the function f(x).... then how much..... is equal to?

[strong furnace]

if I put this in translate would it give me the actual thing?

2.38 设 函 数 f (x) 2.c - 1,> 2 , 则 f (f (f () -5)) 等 于 多 少?

what have you tried @finite marsh

try a different channel maybe @alpine sable

[finite marsh]

this

is what i got

[strong furnace]

let me take a look

[languid ore]

Yo, can someone walk me through this

[strong furnace]

seems correct if you got 7 as the final answer

[finite marsh]

well i am not sure

[strong furnace]

what part are you unsure about ?

[finite marsh]

my friend got x1=-4 ,x2=0

[strong furnace]

2.38 right?

[finite marsh]

yup

[strong furnace]

he got f(5/2) = -4 ?

seems like he got it wrong if that is the case

[finite marsh]

and my other friend got this

[strong furnace]

,rotate

[strong furnace]

he misunderstood what f(5/2)-5 means

it does not mean f(5/2-5)

[finite marsh]

i guess that could be it

how about for 2.37?

[finite marsh]

does the math check out

[strong furnace]

2.37 若 f (x) = J.-2, (r> 0), (<0) 则 f [f (-2)] 等 于 多 少? -2.c + 1, <- 1 -3, - 1 <r <2 translating this for reference

the math and the answer seems correct yes

[finite marsh]

If f(x)=..... then f..... equals to?

okay

Given the function....how much is..... equal to?

is kinda the rough translations of the chinese characters in 2.40 @strong furnace

[strong furnace]

yeah I used translate myself to get just that

this seems correct as well

[finite marsh]

can i send you the rest?

[strong furnace]

how many are there?

you can send them 1 by 1 I guess

[finite marsh]

2.34 and 2.35

[lethal ore]

What's the question?

[strong furnace]

2.34 is correct

[strong furnace]

and so is 2.35

[finite marsh]

kk

[strong furnace]

use a different channel this is busy rn

[finite marsh]

i think 2.39 is not correct

[strong furnace]

this is quite messy I will try to solve it myself and find the answer first

but give me a translate on this one

google kinda failed for this so I need exact translation

[finite marsh]

what did google give you

[strong furnace]

never mind I got it I just copy pasted the wrong thing

it is sum of arithmetic sequence right?

[finite marsh]

yup

[strong furnace]

from your solution I can tell there is a mistake but idk if that reflects in your final answer

S_18-S_15= a_16+a_17+a_18 and not what you wrote

you should get 72 as the answer

[finite marsh]

s18-s15=a16+a17+a18=3a1+48d=18

a1+16d=6 s3=a1+a2+a3=3a1+3d=-6

a1+d=-2

[strong furnace]

negative signs?

[finite marsh]

a1= -38/15 d=8/15 S18=9(a1+a18)=9(2a1+17d)=36

[strong furnace]

wait

[finite marsh]

this is what my friend got

[strong furnace]

my google translate removed the negative signs so even my answer is incorrect

but what your friend has

done

is correct

[finite marsh]

i still dont get it

can you edit my image to see where i fucked up

[strong furnace]

ok you got this right?

[finite marsh]

oh i see

i still got the wrong answer

[strong furnace]

post your work

[finite marsh]

bruh

wait a sec

[strong furnace]

[finite marsh]

my phone does this sometimes

yeah idk it just does not send it properly

i guess if you could write it up i would really appreciate that

its the last question kinda burned out after doing 40 of these

[alpine sable]

Hey

Can someone pls help me with number 13

[strong furnace]

sorry but can't do that atm :/

[finite marsh]

okay

[grand heart]

could someone please explain to me how

is equal to

[finite marsh]

thanks for the help

[alpine sable]

Use euler’s identity

Wait no that’s not necessary

[grand heart]

yeah its basic

[alpine sable]

Just do normal fraction addition

Yea make the denominators common

[lethal ore]

Got the solution or want some help? @grand heart

[young flume]

hello, how do i calculate the average gain when i have 15/25th chance to get nothing, and some other chances to get variable amounts? i've completely forgotten and can't figure it out

[subtle bay]

times the probability by the gain and sum them

e.g. (1/5times5)+(2/5times3)...ect

[paper marlin]

hi, how do i classify sqare root numbers for example: √7

or √64/√100

[subtle bay]

like as in irrational and rational?

[paper marlin]

yes and like intergers, imaginary, whole, ect

[subtle bay]

cause with √7=√4√3

√7=2√3

then imaginary to my knowledge is represented by i as √-1

and with that i^2 is 1

√7 being irrational

[paper marlin]

would it be something like this then

[subtle bay]

8/10

4/5

so 4/5 and real

the other one is real and irational

[paper marlin]

ic ok tyy

[lethal ore]

"@grand heart"

$\frac{1}{1+e^{-x}}\cdot \left(1-\frac{1}{1+e^{-x}}\right)$\
\
$\frac{1}{1+e^{-x}}\cdot \left(\frac{1+e^{-x}-1}{1+e^{-x}}\right)$\
\
$\frac{1+e^{-x}-1}{(1+e^{-x})^{2}}$\
\
$\frac{1}{(1+e^{-x})^{2}}-\frac{1+e^{-x}}{(1+e^{-x})^{2}}$\

[ocean seal]

my name is jeff

[honest lotus]

can anyone here do pre calc ?

[lethal ore]

Writing these equations seems fun 🙂

What's the question?@honest lotus

[lethal ore]

Sorry ☹️ @honest lotus

[young flume]

and then if all probabilities are x/25 then the average gain i got is per 25 items right?

[limpid spade]

did u learn it?

[subtle bay]

yea yea, pretty sure, i was just calculating house edge for a gambling game

[young flume]

alright

[subtle bay]

so i just fed u part of my formula lol

[young flume]

cool, i basically need to calculate how many items i need to reach a certain threshold, but i gain varying amounts per item. thanks for the help

[honest lotus]

idk how to do it

i don’t remember learning

[limpid spade]

learn it

check your course

[honest lotus]

i did she didn’t post any notes

[lethal ore]

Give me a min
I think I've got a clue "@hershey#0957"

[honest lotus]

Okay

[limpid spade]

https://math.libretexts.org/Bookshelves/Linear_Algebra/Book%3A_A_First_Course_in_Linear_Algebra_(Kuttler)/06%3A_Complex_Numbers/6.03%3A_Roots_of_Complex_Numbers

[analog locust]

question

[lethal ore]

"@honest lotus"

[analog locust]

how do I solve this?

and is it a non linear differential equation?

since if I turn it into another form it will be like

y' - (2+x) y^2 = 0

[lethal ore]

"@honest lotus"

[honest lotus]

oh

thank you

[lethal ore]

"@analog locust"

"@analog locust"

[analog locust]

woah thanks... O_O

[lethal ore]

Yw🙂

[analog locust]

ooooh

this is the so called seperable equation, right?

where you go from dy/dx = f(x,y)

into M(x) dx + N(y) dy = 0?

[lethal ore]

Variable separable I guess
I'm not sure @Kenspectacle#9152

[analog locust]

and what is the minimum point of it? @lethal ore

[lethal ore]

Minimum point of the function? @analog locust

[analog locust]

like... do I just derive it again and solve for f'(0)?

yep

[lethal ore]

Yep

[analog locust]

do I derive it in term of x or y?

and if I derive it in term of x... what is d(1/y)/dx?

[lethal ore]

Differentiate with respect to x
Equate it to 0
Find x 🙂🙂🙂

[analog locust]

and why not y? @lethal ore ? 🙂

[lethal ore]

Beautiful question but the answer is too lengthy to text man
I know why but I don't know how or what to type 😅
"@Kenspectacle#9152"

"@analog locust"
Dm me or give me a call if you really wanna know why?

[analog locust]

sure, im eating right now though! @lethal ore 🙂

maybe in like, 10-20 minutes?

[lethal ore]

Your call 🙂

[analog locust]

awesome, thanks man!

[lethal ore]

Happy to help 🙂

[soft flicker]

is anyone any good at differential geometry? i was reading about normal and binormals on curves and came across this problem i couldnt understand.

y is a smooth unit speed curve (y: I to R^3). it has principal normal n and binormal b. assume there exists smooth functions f,g (f,g L I to R^1). with

y = fn + gb. show f^2+g^2=c on entire interval

[upper spruce]

@strong furnace are u there ??

I need ur help

[strong furnace]

plz don't ping man I am busy just post the problem

[upper spruce]

How would u come to know that I need help ?

[strong furnace]

I am not a designated helper read the rules you're not supposed to ping , I don't like to block people so please don't repeat thi

4. If your question has not been answered for a minimum of 15 minutes, you may use the @Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[upper spruce]

I am sorry

[strong furnace]

just wait a bit some1 might decide to help you

[upper spruce]

Yesterday u had explained me well so I thought to ask u

[upper spruce]

<@&286206848099549185>

Pls help

[strong furnace]

bruh

what have you tried?

[vagrant rover]

Did I do this correctly?

Is answer C) correct?

[oak chasm]

Yes.

[spark ibex]

anybody good at definite integrals?

[alpine sable]

U sub

u=lnx
du=1/x dx

Hope that helps

[analog locust]

guys, would it be the same thing?

if you integrate fy(x,y) in respect to y, do you also get f(x,y)?

[tacit jacinth]

hey could i have some help on my graphs of exponential growth? im confused

[shell widget]

just ask

if anyone knows, theyll answer

@analog locust Yes

after integrating f_y (x,y) wrt y, you get f(x,y) + some constant g(x)

[alpine sable]

Here is an equation, it has two horizontal asymptoms.

One of them doesnt exist on the graph, why is that?

[shell widget]

x^2 - x - 6 = x^2 - 3x + 2x - 6 = x(x-3) + 2(x-3) = (x-3)(x+2)

x^2 - 4 = (x+2)(x-2)

[alpine sable]

oh its the right picture

[shell widget]

so the x+2 part cancels out

and ur left with only one (x-2) in the denominator

which means x=2 is a vertical asymptote

[alpine sable]

oooh ok thanks

[shell widget]

although for x=-2, the function isnt defined

[alpine sable]

how did the cos * pi/4 became sqrt2/2? <@&286206848099549185>

[small stag]

Draw a 45-45-90 triangle

Label a leg as 1

Solve for the other leg and the hypotenuse

Then find the cosine of either base angle

Cos(pi/4) is a nice trig value

Remember it

sin, tan, cot, and all their reciprocals

[alpine sable]

I'm sorry, why do I need to label a leg as 1? and how am I supposed to find the leght of the other legs if I do miss the other data? I mean a^2+b^2=c^2 ; if I do have only 1 data, how can I get the leght of the rest?

[small stag]

1 is an easy number to work with

But call it 5 if you want

Also a 45-45-90 is an isosceles triangle

You have all the information you need to find the cosine of 45° or pi/4

[alpine sable]

isn't cos = adj/hypotenuse? how I'm supposed to calculate the legth of each one, if I do know the length of only one leg? I'm sorry I ain't following...

[wary skiff]

The square of the diameter equals the cross-sectional area, d^2 = CM. A cable is checked for a power installation and it is found to be too small. The cable has 37 strands of copper wire, each having a diameter of 82.2 mils. Find the size of the cable in circular mills (CM).

[small stag]

Recall properties of isosceles triangles

[woven knot]

Plzzzzz help

Only have 5 mins and I’m freaking out

These too omfg

I really need help

[alpine sable]

checked the isoscele; but cos45 isn't = sqrt2?

supposing that the lenght of one leg is 1

[haughty wadi]

does this look right

[alpine sable]

channel is occupied, also I can check it if you dm me the iges file, it's hard to tell if the measurements are equal just from a pic

though I can tell (from the pic) that at least one item is missplaced

[lean cobalt]

How do we know when the channel is no longer occupied? Had a question as well

[alpine sable]

"2. Before asking a question, make sure that the channel you are using is not currently in use. An occupied channel would generally have an ongoing discussion or a trailing unanswered question. Likewise, when you are done using a channel, make this clear so that it's open for others to use."

[alpine sable]

Still need help?

You were in a test?

[wary skiff]

The square of the diameter equals the cross-sectional area, d^2 = CM. A cable is checked for a power installation and it is found to be too small. The cable has 37 strands of copper wire, each having a diameter of 82.2 mils. Find the size of the cable in circular mills (CM).

Help

[woven knot]

It’s not really a test just was timed

[alpine sable]

Want the answers?

or

[wary skiff]

An electrician earns $25.30 per hour. During 1 week she works these hours: Monday, 8 hours; Tuesday, 7 hours; Wednesday, 5.5 hours; Thursday 10 hours; and Friday, 4.5 hours. What is her average daily earning? *
3 points

[alpine sable]

just add the hours (8+7+5.5+10+4.5) = 35, multiply 35 for 25.3 = 885.5 , and divide the result for the 5 workin day, and you get the average daily earning ; but my math has problems, so it might be wrong.

[topaz meadow]

can anybody help me with this?

and this?

my teacher doesnt seem to have any lessons on a+bi form

[glass lichen]

You should've learned rectangular form first

[analog locust]

im a bit confused with this

I tried solving it by integrating the fy instead of fx

and I got f(x,y) = y sin x + x^2 e^y - y + h(x)

solving for h(x), gets me y

but the implicitly defined solution is f(x,y) = y sin x + e^2 e^y - 1

what am I doing wrong here?

I got h'(x) = dy/dx btw

is it wrong?

[shell widget]

you have f(x,y) = ysinx + x^2 e^y + h(y), partially differenciating with respect to y, you get f_y (x,y) = sinx + x^2 e^y + h'(y)

[analog locust]

@shell widget but I want to try solving in term of h(x)

to see the soundness of this method lol

and I get f(x,y) = ysinx + e^2 e^y - y + h(x)

[shell widget]

ok so integrate f_y (x,y) = sinx + x^2 e^y - 1 with respect to y, we get f(x,y) = ysinx + x^2 e^y - y + g(x)

[analog locust]

how did I get this "-y"?

yeah that is what happened to me

[shell widget]

Okay so we have f(x,y) = ysinx + x^2 e^y + h(y) and f(x,y) = ysinx + x^2e^y - y + g(x)

comparing, we see that h(y) = -y and g(x) = 0

so f(x,y) = ysinx + x^2 e^y - y

[analog locust]

wait what

why is g(x) = 0?

[shell widget]

compare both the f(x,y)

[analog locust]

lets say I don't know the previous f(x,y)

how do I know that f(x,y) is actually that value?

[shell widget]

wdym?

[analog locust]

f(x,y) = ysinx + x^2 e^y - y

how do I get to this?

[shell widget]

by using either f_x (x,y) or f_y (x,y)

your choice

[analog locust]

I mean, how did I get g(x) = 0?

so I want to use f_y(x,y)

[shell widget]

Okay so we have f(x,y) = ysinx + x^2 e^y + h(y) and f(x,y) = ysinx + x^2e^y - y + g(x)

do u understand till here

[analog locust]

yeah

[shell widget]

both are f(x,y), so both are equal

[analog locust]

but then, how did you know g(x) is equal to 0?

[shell widget]

so we have ysinx + x^2 e^y + h(y) = ysinx + x^2 e^y - y + g(x)

everything cancels out, we are left with h(y) = -y + g(x)

now since h(y) is a function of y and not of x, its clear that it must be equal to -y

and thus we must have g(x) = 0

[analog locust]

wait what?

am I supposed to solve both f_x and f_y?

and why is h(y) equal to -y

[shell widget]

We had f_x (x,y) = ycosx + 2xe^y

It's partially differenciated with respect to x, so "y" was a constant

we integrate partially with respect to x, keeping "y" constant

so we have f(x,y) = ysinx + x^2 e^y + K

[analog locust]

yup

[shell widget]

But since "y" is also a constant, it can appear in the constant of integration

So we remove K and write h(y)

and then h(y) can include constants, doesnt matter

so we have f(x,y) = ysinx + x^2 e^y + h(y)

Okay so now

We have f_y (x,y) = sinx + x^2 e^y - 1

Integrate this with respect to "y", keeping "x" constant

so we have f(x,y) = ysinx + x^2 e^y - y + g(x)

We have f(x,y) = ysinx + x^2 e^y + h(y) and f(x,y) = ysinx + x^2 e^y - y + g(x)

Both are f(x,y), equate them

ysinx + x^2 e^y + h(y) = ysinx + x^2 e^y - y + g(x)

simplify, you get h(y) = -y + g(x)

[analog locust]

alright I understood so far

[shell widget]

h(y) is purely a function of y, it cant have any x

so it must be that h(y) = -y

[analog locust]

why is h(y) purely a function of y?

and why can't g(x) be in it too?

[shell widget]

answer me this

integrate x with respect to x, what do u get

[analog locust]

1/2 x^2?

[shell widget]

+c

but yeah 1/2 x^2 + C

Why not (1/2) x^2 + C + x?

[analog locust]

??

[shell widget]

we just cant

when we're integrating with respect to some variable, then a constant is added(integration constant)

[analog locust]

and what are you trying to say from it?

[shell widget]

and that constant cannot be the variable we are integrating with respect to itself

[analog locust]

ohh

OHHHH

since h(y) is a constant gained from integrating Y

you cannot get a c + y

[shell widget]

no, we get h(y) by integrating with respect to x

and since we are integrating with respect to x, we cannot have our integration constant(which is h(y)) contain x

so h(y) is purely a function of y

h(y) = -y + g(x)

and so h(y) = -y

and so g(x) = 0

in the end, u get f(x,y) = ysinx + x^2 e^y - y + 0

[analog locust]

how do we whether know g(x) contains x?

[shell widget]

same process

[analog locust]

I am sorry, my brain is a bit slow since this is 2 am for me right now

[shell widget]

like h(y) is a function of y, g(x) is a function of x

same idea

constant of integration

[analog locust]

ahhh okay, thanks! 🙂

[foggy rampart]

Can anyone help with a simple prob question, dunno why I'm not getting this

Where does the p=(2/5) come from? that's the only thing I'm confused about

I get that there should be 2 trials left given the info, but don't understand why it's 2/5 instead of 1/3 for l=1

[analog locust]

what should I do if there is a minus behind y'?

I only know of the form when a + is used

like a + b y' = 0

what should I do when its a - b y'?

[shell widget]

Do you mean -(4y-x)?

[analog locust]

yep

[shell widget]

factor out a - from 4y-x

you get -(-(x-4y))

which is just +(x-4y)

[analog locust]

wait you can do that?

O.o

what happens to the y'?

[shell widget]

nothing

what we did is something like this

-(a-b)c = (b-a)c

[analog locust]

..... my brain is so tired

im confused

[shell widget]

u dont get this?

[analog locust]

I don't

[shell widget]

$-(5-10)(20) = --(10-5) = +(10-5)(20) = (10-5)(20)$

[ocean seal]

Sup?

[shell widget]

$-(a-b)(c) = --(b-a) ] = +(b-a)(c) = (b-a)(c)$

[ocean seal]

Sup?

[shell widget]

you should know that (a-b) = -(b-a)

[analog locust]

ahhh okay

makes sense

[vivid rune]

Could someone help me on this

Problem 3

[analog locust]

can anybody explain me this?

[north kettle]

hey so quick question
if ur finding the bearing of x from b
and x is like directly above b
whats the angle of bearing
is it 180 or 360 ?

[shell widget]

@analog locust product rule

[analog locust]

ahhhh okay I got it

umm...another question

d(2x)/dy

is 0 right?

since it is regarded as a constant

or did I understood it wrongly?

[gentle garden]

I don’t understand how they got 70.08

[shell widget]

@analog locust if u mean partial derivative, then yes its 0

[analog locust]

ty

[alpine sable]

the integral subtracts the area under the curve and adds the area above the curve

i think you just integrated from -1 to 6

the function is below the x-axis from -1 to 5

so we need to take the absolute value of that "negative area"

and from 5 to 6 it's above the x axis

[gentle garden]

When do I know when to use addition and subtraction?

[alpine sable]

wdym

[gentle garden]

Like how would I do it by hand

[alpine sable]

adding/subtracting two numbers?

[gentle garden]

The hw told me to find the area function

[alpine sable]

it wants you ti find the grey area

the integral gives you the "signed area"

[gentle garden]

Okay

[alpine sable]

so it adds the area above the x-axis and subtracts the area below the x-axis

but we want to find the total grey area

[gentle garden]

Oh because this is not net area I don’t subtract them

[alpine sable]

so we want the parts that are below the x-axis to be added, not subtracted

[alpine sable]

yes exactly

[gentle garden]

Ah okay

How do you find a area function then

For this equation

[limpid spade]

which

[gentle garden]

My hw told me to use area function to find the area underneath

How do I find the area function

[alpine sable]

this will give you the total area of the grey region

when the function is below the x-axis, the area is negative

from -1 to 5 the function's below the x-axis

so we take the absolute value of that bit to make it positive

and from 5 to 6 it's above the x-axis

so we can leave that part alone

[alpine sable]

oh are you talking about how to evaluate the integrals

[gentle garden]

Yeah

I think

[alpine sable]

so do you remember the power rule in differentiation?

when you integrate polynomials you basically do that in reverse

So

a.express the numerators and dominators as products of prime factors.
b.cancel the common factors.
c.write the lowest terms of the given fraction.
1 .3/6
2 .9/15
3 .24/39
4 .15/21
5 .12/6
6 .4/10
7 .14/24
8. 28/2
9 .60/6
10 .45/81

My answeres are

so the integral of x^3-5x^2 would be (1/4)x^4-(5/3)x^3

[alpine sable]

1.1/3

2.3/5

4.3/7

5.6/3

6.2/6

7.7/6

8.14/1

9.15/3

Is My answers right?

then evaluate (1/4)x^4-(5/3)x^3 at 5 and evaluate it at -1

[alpine sable]

repost this in an unoccupied channel

also don't post the same question in multiple channels

[gentle garden]

That would be the anti derivative of (x^3-5x^2)right?

[alpine sable]

yeah the integral is the antiderivative

[gentle garden]

Yeah

[analog locust]

how do you solve this one?

[shell widget]

try letting y = Vt

[analog locust]

actually the question asks you to prove whether a solution exist using the Picard Lindelöf method

[shell widget]

rip

nvm then

[analog locust]

umm... do you by any chance know what it is?

[shell widget]

its homogenous

thats all i know

[bright saddle]

When I solved this, I got 16. is that right?

[shell widget]

is that 9^(8/x) ?

[bright saddle]

yea

[shell widget]

,w solve 9^(8/x) = 31

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Sup?#7960

[shell widget]

lol

is that really = 31

[bright saddle]

how did it get 31

[shell widget]

It says = 31 in the picture

if it is 9^(8/x) = 3, then yes x = 16 is correct

[bright saddle]

once in log form log9(31)=8/x
how would I solve

[shell widget]

use a calculator

[bright saddle]

do I just put that in

how could I separate x

[tawdry linden]

lemme know if i need to take a better pic

but i kind of have 28 mins to solve this and i have no idea how

[bright saddle]

cant you just factor

[tawdry linden]

is that all i have to do?

[bright saddle]

is the x half of the length/width

[tawdry linden]

i see

i just wasn’t sure

[bright saddle]

well I dont know it doesnt say so it might not be

[tawdry linden]

i’ll try that anyway

thanks

[wheat prawn]

i had a question

on why those 2 equations

are not factorable

[wheat prawn]

<@&286206848099549185>

[void sphinx]

are leslie matricies asymptotic when raised to high powers and multiplied by a vector?

[runic jasper]

can someone enlighten me in this?

[hasty sparrow]

i got y (variable) but I don't know how to write the equation

[woven flume]

@runic jasper did you draw it

[runic jasper]

yes

Im kinda confused

[wheat prawn]

@runic jasper this channel is busy

I had posted my question here

[runic jasper]

mbmb

[wheat prawn]

i had a question
on why those 2 equations
are not factorable

[wheat prawn]

no worries

[hasty sparrow]

<@&286206848099549185> im very uncleared of what to do

[indigo jetty]

they are factorisable as long as you managed to get at least 2 real roots of the equation, just that it does not look like the usual style that you are used to

e.g first one is actually $(x-(1+\sqrt2))(x-(1-\sqrt2))$

[ocean seal]

Ken G

[wheat prawn]

@indigo jetty ik but

cant it be factorable like the 2nd equation

like x-1

[indigo jetty]

the 2nd equation happens to have 2 real and equal roots, which is x = 1, so it can be easily spotted

the first one is much harder

that's why when you can't spot a proper way of factorising, use the quadratic formula

[wheat prawn]

@indigo jetty but u can do the same for the first equation

[indigo jetty]

if you can spot that it's 1+-sqrt2 then go ahead

[wheat prawn]

see

[indigo jetty]

expand it out and see if you get back the same equation

clearly it's wrong

[wheat prawn]

how do u know its not factorable tho

product and sum

factor gets u 2

-1x-1

-2

[indigo jetty]

it's factorisable as long as the equation has 2 real roots. as for how the 2 roots look like, it depends on the equation

nice roots like x =1, 2 etc will make it easy

but most of the time there will be ugly roots like x = 1+- sqrt2 and so on

[wheat prawn]

so to know u will have to expand and check

any time

for these type of equations

[indigo jetty]

expand and verify

[wheat prawn]

ok

[indigo jetty]

if they do not match, then the factorisation is wrong

[raw inlet]

can someone help me solve this, this is calc related rates

[alpine sable]

ok so let's let the 5000m side be a, the distance from the plane to airport A be b, and the distance from the plane to airport B be c

c^2=a^2+b^2-2abcos(c)

when we differentiate both sides the a^2 term goes away

it's a constant

it doesn't change, it's derivative is 0

[raw inlet]

ohhhh

[alpine sable]

so we have
2c dc/dt=2b db/dt -2*5000cos(130) db/dt

db/dt = 84

so now we just need to find c

[raw inlet]

would we do 84(120) to find one of the sides?

then we can plug it into the formula and solve for the unknown vairable?

[alpine sable]

so two minutes after leaving a, what is the distance from airport A to the plane?

[alpine sable]

yup

[raw inlet]

okok

[alpine sable]

exactly

[raw inlet]

I SEEEEEE tyty very much

[vocal mural]

Hi
I have a question
Okay so I'm trying to find the orthocenter of a triangle
With points (-4,-6), (10,5), and (6,-5)
I got y = -14/11x + -122/11 for line AD
And y=-10/1x + 55 for line CE
But when these two lines intersect, the point of intersection isn't the correct solution?

[alpine sable]

wolfram alpha is helpful for checking solutions for bashy problems like this

[raw inlet]

im confused, where did "ab" go next to -2?

[alpine sable]

differentiating -2abcos(c) with respect to time:
substitute a=5000 and angle c=130 degrees
-10000cos(130)*b
use chain rule here since b is a function of time
-10000cos(130)*db/dt

[raw inlet]

OHHHHHHHHHHHHHHHH

u r so SMARTTT

ty very much

[crude moth]

hi is this open

[raw inlet]

wait im confused one more time sorry 😅 , anyways why does a^2 is a 0, but -2a isnt

[alpine sable]

so derivative of 5000^2 with respect to time is 0, but in the second case the -2a is multiplied by b

like how the derivative of 5 is 0 but the derivative of 5x is 5

[raw inlet]

ohhhh

i see okok thank very much

[uncut osprey]

Constants have a derivative of 0. But coefficients don't

[alpine sable]

yeah that's a better way of wording it

[raw inlet]

ty yall

[hollow oriole]

hello im trying to solve arcsin(sin(-4pi/5)) how would i go about this

[alpine sable]

What's the range of arcsin?

[hollow oriole]

-pi/2 to pi/2?

[wise jewel]

how do i solve both of these?

i have absolutely no clue what to do on either :/

[woven flume]

since the sides are equal pairs

the opposite angles add up to 180

for 19

[lethal ore]

Nope "@woven flume"

[woven flume]

oh nvm didn't realize they aren't all equal

sorry

[barren bolt]

a good tip for these kinds of questions is to divide the shapes into right triangles

[woven flume]

the angle opposite to 96 is also 96 right?

[lethal ore]

Yep

[woven flume]

yeah that's what I mixed it up with

so a quadrilateral sums to 360

so 360-96-96 = 168

therefore the sum of the other 2 angles is 168

[hollow oriole]

@alpine sable?

[lethal ore]

"@wise jewel"\
$12x-9=17x+3$\
$5x=-12$\
$x=-\frac{12}{5}$

[ocean seal]

my name is jeff

[wise jewel]

wait im confused as to why they'd be equal to each other

if i split them into two triangles horizontally

they're both different sizes

[lethal ore]

Split them into two triangles vertically @wise jewel

[alpine sable]

Yeah, since -4pi/5 is not in that, we need to change the angle inside the sine so that the new angle is there.

[hollow oriole]

ok gotcha

[alpine sable]

Think of using some sine identities

[ocean seal]

Azaradichta

[hollow oriole]

hm would i be able to add pi?

[alpine sable]

No because it will make sine negative

But you can add it and take a minus sign

[ocean seal]

Azaradichta

[alpine sable]

Now use the fact that sine is an odd function.

@hollow oriole

[young ocean]

I got 50.13 as the perimeter but apparently its wrong, can someone do this and tell me if they get a diff answer? thanks

[fading zephyr]

you have a triangle for which the angles are 36, 90, 54, and a height of 6.9

should be able to work out the base from that, and the perimeter should be 10x that base length

[arctic delta]

can someone explain what was done to simplify here

[sly mantle]

$\frac{a+b}c=\frac ac+\frac bc$

[ocean seal]

RokabeJintaro

[arctic delta]

whered the 2x^3/2 come from

[sly mantle]

$x\sqrt x=x^1x^{1/2}=x^{3/2}$

[ocean seal]

RokabeJintaro

[arctic delta]

right i forgot about that

[young ocean]

Thats what i did, and i got 50.13, its still being marked as wrong... heres my work, did i do anything wrong?

[gray isle]

your calculator isn't in degrees

[young ocean]

? wdym

[fading zephyr]

which calcultor are you using? the windows one?

[young ocean]

yeah

[gray isle]

there are two main ways to measure angles,
in radians and in degrees

[gray isle]

some calculators use radians by default

[fading zephyr]

make sure you click that thing until is says DEG

[young ocean]

yep, it is

its using DEG

[gray isle]

however in your triangle it is implied that the angle is 36°

,w 6.9tan(36 degrees)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ramonov#0921

[gray isle]

wtf

[fading zephyr]

hahaha

[gray isle]

fml

wtf u doing wolfram

[young ocean]

hmm, welp ig i didnt do anything wrong... maybe its a teacher grading error

[fading zephyr]

ribbid, please use an empty channel

lemme check really quick

[young ocean]

k

[light coyote]

oh this wasn't empty? .. sorry no one was typing so I thought it was empty

[fading zephyr]

i guess i do get ~50.1 as well

maybe ramonov can corroborate

[gray isle]

1 sec

hmm yeh. didn't read the whole chat.

maybe they want the exact perimeter

[young ocean]

like no rounding?

[gray isle]

yeh, there's an exact value for tan(36°)

its a bit ugly though

,w tan(36°) exact

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ramonov#0921

[fading zephyr]

aha

[young ocean]

ok welp sadly my teacher grades wrongly quite often, so its probably just that. Thanks anyway guys for your help

[fading zephyr]

you can email and ask what exactly the wanted, at least for future reference

[young ocean]

yeah ill ask in person tmrw

[sonic trellis]

Is this open?

[gray isle]

yes

[sonic trellis]

Cool

This might sound dumb but what is the difference between a tangent and a sine

[halcyon sleet]

do you mean the functions?

[sonic trellis]

yup

[halcyon sleet]

lol sorry if i take a bit im not great at explaining stuff

[sonic trellis]

Its okay

[halcyon sleet]

so imagine you can make a right triangle where the hypotenuse can be slanted at a different angle, like imagine changing the angle to make it lift up and down

but (i think?) for the purposes of this just imagine the length of the hypotenuse stays the same

so like at a really high angle, close to 90 degrees, the vertical part of the triangle is really long and the horizontal part is really short

but at a really small angle, close to 0 degrees, the horizontal part of the triangle is really long and the vertical part is really short

the number you get when you plug that angle into the sine function gives you the ratio of the length of the vertical part to the length of the hypotenuse

and then cosine is similar, but instead it's the ratio of the length of the horizontal part to the length of the hypotenuse

[sonic trellis]

so

Sine is the vertical

and cosine is the horizontal

[halcyon sleet]

yeah basically

[sonic trellis]

what about tangent

[halcyon sleet]

sine is opposite side to the angle, cosine is adjacent side to the angle

tangent is the ratio of the length of the vertical side to the length of the horizontal side

[sonic trellis]

so so basically

vertical over horizontal

or vice versa

[halcyon sleet]

just vertical over horizontal

[sonic trellis]

Ok

thank you sir

[halcyon sleet]

so if u think about having a 90 degree angle

[sonic trellis]

or maam

[halcyon sleet]

then the vertical part will just be the same length as the hypotenuse, so that's why sin(90) = 1

[halcyon sleet]

the little picture i drew shows why it's not always the vertical, the best way to think about it is opposite side/hypotenuse = sin(angle)

[sonic trellis]

oh

[halcyon sleet]

because in the top triangle, where the angle is in the bottom left, the vertical is opposite from the angle

for sine, you use the side that isn't touching the angle

the green one

since it's on the opposite side of the triangle for the angle

and then cosine is always the adjacent side to the angle, the one that's touching the angle

that way no matter where the angle is, it's always:

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite/adjacent

[sonic trellis]

You are a legend

thank you

[halcyon sleet]

and if u think about the numbers u get from those functions, it's just the ratio of those sides

like how tan(45) = 1 because the opposite and adjacent sides are the same length, so dividing them gives you 1

and how sin(90) = 1 and cosine(90) = 0, because if u think about it like the first triangle (angle in bottom left), then the opposite side is as long as the hypotenuse would be if it pointed straight upwards, and the adjacent side isn't even there because the hypotenuse doesn't go to the side at all

and so that's why tan(90) is undefined, because the length of the adjacent/horizontal side is 0 and you can't divide by 0

[halcyon sleet]

it might not be the perfect explanation, but I hope it helped

[sonic trellis]

It did

thank you

[halcyon sleet]

cool

do you mind if I ask a question in here now?

[sonic trellis]

Not at all

its free

[halcyon sleet]

cool

I can rewrite the equation as [5 7 9]_B = [7 8 9], right?

since they have the same basis would it just work like normal vector addition?

and then to solve I would just solve the normal way for a change of basis matrix?

[ruby current]

i think so

you can always check your answer by verifying that the statement holds

[halcyon sleet]

i'll try lol but i feel like i don't have a good enough understanding of the content to do that haha

[ruby current]

i'm also taking linalg so i'm not an expert

[halcyon sleet]

all good, just nice to know that someone thinks it's correct too

[north jungle]

wait is this channel taken

[halcyon sleet]

nah ur good

[north jungle]

alr

how do i solve this

[halcyon sleet]

you would just take the base and height as the lengths of those sides

[north jungle]

so

uh

[halcyon sleet]

when you normally solve for the area of a triangle, it's just like the bottom left corner is at (0,0)

so the base and height are really like you're subtracting 0 from those numbers

so here the base would be 11-2 and the height would be 5-2

then u can just plug those numbers into the regular formula for area triangle

[north jungle]

ohh

then after

9 times 3

27

[halcyon sleet]

yeah but that would give u the area of the rectangle around the triangle

[north jungle]

then what

[halcyon sleet]

this shows how it would make a rectangle

is that clear or should i explain more

[upper kayak]

basically what he means is that a triangle is always half of some rectangle

suppose you have a rectangle with length 3 width 4

the area is 12

now if you slice it in half diagonally

you get a triangle with area

$\frac{l \times b}{2}$

[ocean seal]

gang

[upper kayak]

where l and b are the original rectangle's length and breadth respectively

and the triangle is half of that

that's where 1/2 bh comes from

[north jungle]

uh

ohh

wait

so its 6

for the supposively rectangel with 3 and 4

so wait what would the answer be

16.5?

[upper kayak]

you can think of any triangle as half of a rectangle

[flat quest]

hi

[upper kayak]

the area of the red triangle above is half of 3 x 4

[north jungle]

ye

[upper kayak]

which is 6

[north jungle]

yea

[upper kayak]

so think of your triangle here

[north jungle]

i multiplied 11 and 3

[alpine sable]

Usually you wouldn't have to think of a rectangle

and stuff

You could just use Heron's Formula

all you need is the 3 sides

[upper kayak]

bruh

[north jungle]

oh wait i did it wrong

[upper kayak]

yeah the length is not 11

the base starts at x = 2 and ends at x = 11

[north jungle]

so 9?

[upper kayak]

so the length of the base is 9

yes

[north jungle]

then its 3 times 9

right

[upper kayak]

then divided by 2

[north jungle]

which is 13.5

[upper kayak]

3 times 9 gets you a rectangle's area

[fervent grail]

Pls helo

[north jungle]

channels taken

[upper kayak]

the triangle is half of that

[north jungle]

so 13.5?

[upper kayak]

yeah that's correct

yeah

[north jungle]

alr

this is 9 and 3 right

just making sure

[upper kayak]

yeah

i hope you understand where the formula comes from

[alpine sable]

anyone online?

no

all 30K people are sleeping